If all you need is to turn all the LEDs on/off using PWM, you can attach the N-chan MOSFET between the common cathode and ground. Here's an example circuit, ignoring LED current limiting schemes for now.
simulate this circuit – Schematic created using CircuitLab
If what you want is to control individual LED's, then you might still be able to use an N-Chan MOSFET, but your control signal will need to be at least Vthresh above the source voltage to turn the LEDs on. Alternatively, if you have use an up-stream P-Chan MOSFET, your control signal will need to be at least the level of the source voltage to turn the LEDs off (this is the MOSFET pin source voltage, not supply voltage).
If your micro is not able to achieve either of these levels, you can use a second transistor to drive the transistor in series with the LED(s).
Here's a basic example which uses a P-chan MOSFET to drive the LED's, and a N-chan MOSFET/pullup resistor to control the P-chan MOSFET: (again, ignoring any LED current limiting schemes)
simulate this circuit
Resistor values were chosen semi-arbitrarily. You can probably get away with anywhere from 1k up to 100k. Smaller values will draw more supply current when the N-chan MOSFET is on, larger values are more susceptible to noise when the N-chan MOSFET is off.
Best Answer
If you examine your picture it is for a drain current of 31 amps: -
And clearly, if you look at figure 1 in the DS you will never get gate-source voltages of 3 volts or 3.5 volts able to produce a drain current of 31 amps.
With a 3 volts gate source voltage and a more moderate drain current of (say) 1 amp the DS volt drop will be typically 0.1 volts and the power dissipated will be 0.3 watts. Use the 2nd picture for detailed analysis of power dissipation with different gate-source voltages.